The refpages say "Returns the weighted average of the four texture elements that are closest to the specified texture coordinates." How exactly are they weighted? And what about 3D textures, does it still only use 4 texels for interpolation or more?
in 2D textures are 4 samples used which means bi-linear interpolation so 3x linear interpolation. The weight is the normalized distance of target texel to its 4 neighbors.
So for example you want the texel at
(s,t)=(0.21,0.32)
but the texture nearby texels has coordinates:
(s0,t0)=(0.20,0.30)
(s0,t1)=(0.20,0.35)
(s1,t0)=(0.25,0.30)
(s1,t1)=(0.25,0.35)
the weights are:
ws = (s-s0)/(s1-s0) = 0.2
wt = (t-t0)/(t1-t0) = 0.4
so linear interpolate textels at s direction
c0 = texture(s0,t0) + (texture(s1,t0)-texture(s0,t0))*ws
c1 = texture(s0,t1) + (texture(s1,t1)-texture(s0,t1))*ws
and finally in t direction:
c = c0 + (c1-c0)*wt
where texture(s,t) returns texel color at s,t while the coordinate corresponds to exact texel and c is the final interpolated texel color.
In reality the s,t coordinates are multiplied by the texture resolution (xs,ys) which converts them to texel units. after that s-s0 and t-t0 is already normalized so no need to divide by s1-s0 and t1-t0 as they are booth equal to one. so:
s=s*xs; s0=floor(s); s1=s0+1; ws=s-s0;
t=t*ys; t0=floor(t); t1=t0+1; wt=t-t0;
c0 = texture(s0,t0) + (texture(s1,t0)-texture(s0,t0))*ws;
c1 = texture(s0,t1) + (texture(s1,t1)-texture(s0,t1))*ws;
c = c0 + (c1-c0)*wt;
I never used 3D textures before but in such case it use 8 textels and it is called tri-linear interpolation which is 2x bi-linear interpolation simply take 2 nearest textures and compute each with bi-linear interpolation and the just compute the final texel by linear interpolation based on the u coordinate in the exact same way ... so
u=u*zs; u0=floor(u); u1=u0+1; wu=u-u0;
c = cu0 + (cu1-cu0)*wu;
where zs is count of textures, cu0 is result of bi-linear interpolation in texture at u0 and cu1 at u1. This same principle is used also for mipmaps...
All the coordinates may have been offseted by 0.5 texel and also the resolution multiplication can be done with xs-1 instead of xs based on your clamp settings ...